Orthogonality catastrophe beyond bosonization from post-selection

TL;DR

This paper explores how post-selected measurements induce dynamics in a one-dimensional fermionic system that go beyond traditional bosonization, revealing a crossover from reversible to irreversible behavior depending on fermion density.

Contribution

It introduces a non-Hermitian model of fermionic dynamics with post-selection, demonstrating a density-dependent crossover beyond bosonization in low-dimensional quantum systems.

Findings

Reversible dynamics at high density described by bosonization.

Irreversible behavior emerges at low density, breaking bosonization validity.

Crossover is non-perturbative in measurement rate, observable at shallow rates.

Abstract

We show that the dynamics induced by post-selected measurements can serve as a controlled route to access physical processes beyond the boundaries of Tomonaga-Luttinger liquid physics. We consider a one-dimensional fermionic wire whose dynamics results from a sequence of weak measurements of the fermionic density at a given site, interspersed with unitary hopping dynamics. This realizes a non-Hermitian variant of the celebrated instance of a local scatterer in a fermionic system and its ensuing orthogonality catastrophe. We observe a distinct crossover in the system's time evolution as a function of the fermion density. In the high-density regime, reminiscent of the Hermitian case, a bosonized version of the model properly describes the dynamics while, as we delve into the low-density regime, the validity of bosonization breaks down, giving rise to irreversible behavior. Notably, this crossover from reversible to irreversible dynamics is non-perturbative in the measurement rate and can manifest itself even with relatively shallow measurement rates, provided that the system's density remains below the crossover threshold. Our results render a conceptually transparent model for exploring non-perturbative effects beyond bosonization, which could be used as a stepping stone to explore novel routes for the control of non-linear dynamics in low-dimensional quantum systems.